But with European Union heads growing increasingly impatient at the political paralysis in Westminster, they could offer just a shorter postponement - or a longer period of up to a year.
It's a pre-emptive move, even though the contentious Brexit is now delayed and no clear date has been set when Britain will leave the bloc.
The passports started appearing from March 30, which would have been the day after the United Kingdom left the European Union had Brexit gone ahead as originally planned.
Susan Hindle Barone told the Press Association she thought the design should not change as long as the United Kingdom remained part of the EU.
Britain's original withdrawal was scheduled for March 29.
Britain's interior ministry meanwhile confirmed that some newly issued passports now omit references to the European Union on the cover, while others still bear the bloc's name. Passports produced after that date don't have the "EU" label on their burgundy front cover.
Theresa May has written to European Council President Donald Tusk to request an extension to 30 June.
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But the other 27 members must give unanimous backing to any further postponement and are increasingly impatient at the paralysis in Westminster. Both passports are "equally valid for travel", the ministry added.
The Home Office issued a statement saying that the removal of the words "European Union" was part of a redesign process that will see the old dark blue British passports being reissued from late 2019.
The Home Office has confirmed that some passports introduced after March 30 no longer include references to the EU.
The Home Office have said that the old versions will still be sent out until stocks run out "in order to achieve best value to the taxpayer".
British passports have become ensnared in the country's Brexit divisions after the government announced in 2017 it would return to traditional blue passports "to restore national identity".
While Tom Hatton tweeted: "You're lucky when I renewed earlier this year, I received one with European Union still spat on it!" Britain switched to burgundy in 1988 in line with most other countries' passports in what was then the European Community.
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